Two lines are drawn parallel to the diagonal of a square of area $25 c m^{2}$ as shown in the first figure. Another set of parallel lines are drawn along the second diagonal to form a larger square as shown in the second figure, then the area of the larger square is _____.

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If the extremities of a diagonal of a square are (1,−2,3) and (4,2,3) then the area of the square is

The correct option is C 252If a is the length of a side of square then the length of diagonal is given by √2a. Distance between two given points is √(1−4)2+(−2−2)2+(3−3)2=5=√2a. Hence the area is given by a2=252.

If the extremities of a diagonal of a square are $(1, - 2, 3)$ and $(4, 2, 3)$ then the area of the square is

The correct option is C $\frac{25}{2}$
If $a$ is the length of a side of square then the length of diagonal is given by $\sqrt{2} a$ . Distance between two given points is $\sqrt{(1 - 4)^{2} + (- 2 - 2)^{2} + (3 - 3)^{2}} = 5 = \sqrt{2} a$ . Hence the area is given by $a^{2} = \frac{25}{2}$ .